LMFDB - Embedded newform 441.4.e.x.226.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,4,Mod(226,441)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("441.226");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	441.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$26.0198423125$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 19x^{6} + 319x^{4} + 798x^{2} + 1764 $ x^8 + 19x^6 + 319x^4 + 798*x^2 + 1764
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.3
Root			$-0.799027 - 1.38396i$ of defining polynomial
Character	$\chi$	$=$	441.226
Dual form			441.4.e.x.361.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.799027 - 1.38396i) q^{2} +(2.72311 + 4.71657i) q^{4} +(9.14584 - 15.8411i) q^{5} +21.4878 q^{8} +O(q^{10})$	\(q+(0.799027 - 1.38396i) q^{2} +(2.72311 + 4.71657i) q^{4} +(9.14584 - 15.8411i) q^{5} +21.4878 q^{8} +(-14.6156 - 25.3149i) q^{10} +(-30.6336 - 53.0590i) q^{11} -32.4462 q^{13} +(-4.61555 + 7.99438i) q^{16} +(-40.6644 - 70.4329i) q^{17} +(-10.4542 + 18.1072i) q^{19} +99.6206 q^{20} -97.9084 q^{22} +(16.8655 - 29.2119i) q^{23} +(-104.793 - 181.507i) q^{25} +(-25.9254 + 44.9041i) q^{26} +52.0227 q^{29} +(96.9622 + 167.943i) q^{31} +(93.3271 + 161.647i) q^{32} -129.968 q^{34} +(133.578 - 231.363i) q^{37} +(16.7064 + 28.9364i) q^{38} +(196.524 - 340.390i) q^{40} -203.176 q^{41} -21.9520 q^{43} +(166.838 - 288.971i) q^{44} +(-26.9520 - 46.6822i) q^{46} +(-123.961 + 214.706i) q^{47} -334.929 q^{50} +(-88.3547 - 153.035i) q^{52} +(-70.4131 - 121.959i) q^{53} -1120.68 q^{55} +(41.5676 - 71.9971i) q^{58} +(-110.734 - 191.797i) q^{59} +(326.263 - 565.104i) q^{61} +309.902 q^{62} +224.435 q^{64} +(-296.748 + 513.983i) q^{65} +(-302.239 - 523.493i) q^{67} +(221.468 - 383.593i) q^{68} +716.031 q^{71} +(194.438 + 336.777i) q^{73} +(-213.465 - 369.731i) q^{74} -113.872 q^{76} +(144.871 - 250.923i) q^{79} +(84.4263 + 146.231i) q^{80} +(-162.343 + 281.186i) q^{82} +115.652 q^{83} -1487.64 q^{85} +(-17.5403 + 30.3806i) q^{86} +(-658.249 - 1140.12i) q^{88} +(469.682 - 813.513i) q^{89} +183.707 q^{92} +(198.096 + 343.112i) q^{94} +(191.225 + 331.212i) q^{95} -120.394 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{4}+O(q^{10}) $ 8 * q - 6 * q^4	$ 8 q - 6 q^{4} + 22 q^{10} - 204 q^{13} + 102 q^{16} + 222 q^{19} - 172 q^{22} - 366 q^{25} + 220 q^{31} - 2040 q^{34} + 374 q^{37} + 822 q^{40} - 1676 q^{43} - 1716 q^{46} - 40 q^{52} - 5020 q^{55} + 1694 q^{58} + 1332 q^{61} - 1372 q^{64} - 1890 q^{67} + 1750 q^{73} - 4912 q^{76} - 8 q^{79} + 2480 q^{82} - 2232 q^{85} - 2682 q^{88} - 1416 q^{94} - 6020 q^{97}+O(q^{100}) $ 8 * q - 6 * q^4 + 22 * q^10 - 204 * q^13 + 102 * q^16 + 222 * q^19 - 172 * q^22 - 366 * q^25 + 220 * q^31 - 2040 * q^34 + 374 * q^37 + 822 * q^40 - 1676 * q^43 - 1716 * q^46 - 40 * q^52 - 5020 * q^55 + 1694 * q^58 + 1332 * q^61 - 1372 * q^64 - 1890 * q^67 + 1750 * q^73 - 4912 * q^76 - 8 * q^79 + 2480 * q^82 - 2232 * q^85 - 2682 * q^88 - 1416 * q^94 - 6020 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.799027	−	1.38396i	0.282499	−	0.489302i	−0.689501	−	0.724285i	$-0.742170\pi$
$2$	0.799027	−	1.38396i	0.282499	−	0.489302i	0.972000	+	0.234983i	$0.0755034\pi$
$3$		0			0
$3$		0			0
$4$	2.72311	+	4.71657i	0.340389	+	0.589571i
$5$	9.14584	−	15.8411i	0.818029	−	1.41687i	−0.0891033	−	0.996022i	$-0.528400\pi$
$5$	9.14584	−	15.8411i	0.818029	−	1.41687i	0.907132	−	0.420846i	$-0.138267\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	21.4878			0.949635
$9$		0			0
$10$	−14.6156	−	25.3149i	−0.462184	−	0.800527i
$11$	−30.6336	−	53.0590i	−0.839672	−	1.45435i	−0.890169	−	0.455630i	$-0.849414\pi$
$11$	−30.6336	−	53.0590i	−0.839672	−	1.45435i	0.0504975	−	0.998724i	$-0.483919\pi$
$12$		0			0
$13$	−32.4462			−0.692228			−0.346114	−	0.938192i	$-0.612499\pi$
$13$	−32.4462			−0.692228			−0.346114	+	0.938192i	$0.612499\pi$
$14$		0			0
$15$		0			0
$16$	−4.61555	+	7.99438i	−0.0721180	+	0.124912i
$17$	−40.6644	−	70.4329i	−0.580152	−	1.00485i	−0.995461	−	0.0951718i	$-0.969660\pi$
$17$	−40.6644	−	70.4329i	−0.580152	−	1.00485i	0.415309	−	0.909680i	$-0.363673\pi$
$18$		0			0
$19$	−10.4542	+	18.1072i	−0.126230	+	0.218636i	−0.922213	−	0.386682i	$-0.873621\pi$
$19$	−10.4542	+	18.1072i	−0.126230	+	0.218636i	0.795983	+	0.605319i	$0.206954\pi$
$20$	99.6206			1.11379
$21$		0			0
$22$	−97.9084			−0.948825
$23$	16.8655	−	29.2119i	0.152900	−	0.264831i	−0.779392	−	0.626536i	$-0.784472\pi$
$23$	16.8655	−	29.2119i	0.152900	−	0.264831i	0.932292	+	0.361705i	$0.117805\pi$
$24$		0			0
$25$	−104.793	−	181.507i	−0.838343	−	1.45205i
$26$	−25.9254	+	44.9041i	−0.195554	+	0.338709i
$27$		0			0
$28$		0			0
$29$	52.0227			0.333116			0.166558	−	0.986032i	$-0.446735\pi$
$29$	52.0227			0.333116			0.166558	+	0.986032i	$0.446735\pi$
$30$		0			0
$31$	96.9622	+	167.943i	0.561772	+	0.973017i	0.997342	+	0.0728626i	$0.0232135\pi$
$31$	96.9622	+	167.943i	0.561772	+	0.973017i	−0.435570	+	0.900155i	$0.643453\pi$
$32$	93.3271	+	161.647i	0.515564	+	0.892983i
$33$		0			0
$34$	−129.968			−0.655568
$35$		0			0
$36$		0			0
$37$	133.578	−	231.363i	0.593515	−	1.02800i	−0.400240	−	0.916410i	$-0.631073\pi$
$37$	133.578	−	231.363i	0.593515	−	1.02800i	0.993755	−	0.111587i	$-0.0355935\pi$
$38$	16.7064	+	28.9364i	0.0713194	+	0.123529i
$39$		0			0
$40$	196.524	−	340.390i	0.776829	−	1.34551i
$41$	−203.176			−0.773921			−0.386960	−	0.922096i	$-0.626475\pi$
$41$	−203.176			−0.773921			−0.386960	+	0.922096i	$0.626475\pi$
$42$		0			0
$43$	−21.9520			−0.0778523			−0.0389262	−	0.999242i	$-0.512394\pi$
$43$	−21.9520			−0.0778523			−0.0389262	+	0.999242i	$0.512394\pi$
$44$	166.838	−	288.971i	0.571630	−	0.990092i
$45$		0			0
$46$	−26.9520	−	46.6822i	−0.0863882	−	0.149629i
$47$	−123.961	+	214.706i	−0.384713	+	0.666343i	−0.991729	−	0.128346i	$-0.959033\pi$
$47$	−123.961	+	214.706i	−0.384713	+	0.666343i	0.607016	+	0.794690i	$0.292366\pi$
$48$		0			0
$49$		0			0
$50$	−334.929			−0.947324
$51$		0			0
$52$	−88.3547	−	153.035i	−0.235627	−	0.408117i
$53$	−70.4131	−	121.959i	−0.182490	−	0.316082i	0.760238	−	0.649645i	$-0.225082\pi$
$53$	−70.4131	−	121.959i	−0.182490	−	0.316082i	−0.942728	+	0.333563i	$0.891749\pi$
$54$		0			0
$55$	−1120.68			−2.74750
$56$		0			0
$57$		0			0
$58$	41.5676	−	71.9971i	0.0941050	−	0.162995i
$59$	−110.734	−	191.797i	−0.244344	−	0.423217i	0.717603	−	0.696453i	$-0.245239\pi$
$59$	−110.734	−	191.797i	−0.244344	−	0.423217i	−0.961947	+	0.273236i	$0.911906\pi$
$60$		0			0
$61$	326.263	−	565.104i	0.684815	−	1.18613i	−0.288680	−	0.957426i	$-0.593216\pi$
$61$	326.263	−	565.104i	0.684815	−	1.18613i	0.973495	−	0.228709i	$-0.0734503\pi$
$62$	309.902			0.634800
$63$		0			0
$64$	224.435			0.438349
$65$	−296.748	+	513.983i	−0.566263	+	0.980796i
$66$		0			0
$67$	−302.239	−	523.493i	−0.551110	−	0.954551i	−0.998195	−	0.0600592i	$-0.980871\pi$
$67$	−302.239	−	523.493i	−0.551110	−	0.954551i	0.447085	−	0.894492i	$-0.352462\pi$
$68$	221.468	−	383.593i	0.394954	−	0.684081i
$69$		0			0
$70$		0			0
$71$	716.031			1.19686			0.598431	−	0.801174i	$-0.295791\pi$
$71$	716.031			1.19686			0.598431	+	0.801174i	$0.295791\pi$
$72$		0			0
$73$	194.438	+	336.777i	0.311743	+	0.539956i	0.978740	−	0.205105i	$-0.0657537\pi$
$73$	194.438	+	336.777i	0.311743	+	0.539956i	−0.666996	+	0.745061i	$0.732420\pi$
$74$	−213.465	−	369.731i	−0.335334	−	0.580816i
$75$		0			0
$76$	−113.872			−0.171869
$77$		0			0
$78$		0			0
$79$	144.871	−	250.923i	0.206319	−	0.357355i	−0.744233	−	0.667920i	$-0.767185\pi$
$79$	144.871	−	250.923i	0.206319	−	0.357355i	0.950552	+	0.310565i	$0.100518\pi$
$80$	84.4263	+	146.231i	0.117989	+	0.204363i
$81$		0			0
$82$	−162.343	+	281.186i	−0.218632	+	0.378681i
$83$	115.652			0.152946			0.0764728	−	0.997072i	$-0.475634\pi$
$83$	115.652			0.152946			0.0764728	+	0.997072i	$0.475634\pi$
$84$		0			0
$85$	−1487.64			−1.89832
$86$	−17.5403	+	30.3806i	−0.0219932	+	0.0380933i
$87$		0			0
$88$	−658.249	−	1140.12i	−0.797382	−	1.38111i
$89$	469.682	−	813.513i	0.559395	−	0.968901i	−0.438152	−	0.898901i	$-0.644367\pi$
$89$	469.682	−	813.513i	0.559395	−	0.968901i	0.997547	−	0.0699997i	$-0.0222998\pi$
$90$		0			0
$91$		0			0
$92$	183.707			0.208182
$93$		0			0
$94$	198.096	+	343.112i	0.217362	+	0.376482i
$95$	191.225	+	331.212i	0.206519	+	0.357701i
$96$		0			0
$97$	−120.394			−0.126022			−0.0630110	−	0.998013i	$-0.520070\pi$
$97$	−120.394			−0.126022			−0.0630110	+	0.998013i	$0.520070\pi$
$98$		0			0
$99$		0			0
$100$	570.725	−	988.525i	0.570725	−	0.988525i
$101$	640.502	+	1109.38i	0.631013	+	1.09295i	0.987345	+	0.158587i	$0.0506938\pi$
$101$	640.502	+	1109.38i	0.631013	+	1.09295i	−0.356332	+	0.934359i	$0.615973\pi$
$102$		0			0
$103$	265.669	−	460.153i	0.254147	−	0.440196i	−0.710516	−	0.703681i	$-0.751539\pi$
$103$	265.669	−	460.153i	0.254147	−	0.440196i	0.964664	+	0.263485i	$0.0848718\pi$
$104$	−697.198			−0.657364
$105$		0			0
$106$	−225.048			−0.206213
$107$	−66.6758	+	115.486i	−0.0602411	+	0.104341i	−0.894573	−	0.446922i	$-0.852520\pi$
$107$	−66.6758	+	115.486i	−0.0602411	+	0.104341i	0.834332	+	0.551262i	$0.185854\pi$
$108$		0			0
$109$	108.884	+	188.593i	0.0956811	+	0.165725i	0.909893	−	0.414844i	$-0.136164\pi$
$109$	108.884	+	188.593i	0.0956811	+	0.165725i	−0.814212	+	0.580568i	$0.802830\pi$
$110$	−895.455	+	1550.97i	−0.776166	+	1.34436i
$111$		0			0
$112$		0			0
$113$	−2006.09			−1.67006			−0.835031	−	0.550204i	$-0.814550\pi$
$113$	−2006.09			−1.67006			−0.835031	+	0.550204i	$0.814550\pi$
$114$		0			0
$115$	−308.499	−	534.335i	−0.250153	−	0.433278i
$116$	141.664	+	245.369i	0.113389	+	0.196396i
$117$		0			0
$118$	−353.917			−0.276108
$119$		0			0
$120$		0			0
$121$	−1211.34	+	2098.10i	−0.910097	+	1.57633i
$122$	−521.386	−	903.067i	−0.386919	−	0.670163i
$123$		0			0
$124$	−528.078	+	914.658i	−0.382442	+	0.662409i
$125$	−1547.22			−1.10710
$126$		0			0
$127$	1638.92			1.14512			0.572562	−	0.819861i	$-0.305950\pi$
$127$	1638.92			1.14512			0.572562	+	0.819861i	$0.305950\pi$
$128$	−567.287	+	982.570i	−0.391731	+	0.678498i
$129$		0			0
$130$	474.220	+	821.372i	0.319937	+	0.554147i
$131$	45.8755	−	79.4587i	0.0305967	−	0.0529950i	−0.850322	−	0.526263i	$-0.823593\pi$
$131$	45.8755	−	79.4587i	0.0305967	−	0.0529950i	0.880918	+	0.473268i	$0.156926\pi$
$132$		0			0
$133$		0			0
$134$	−965.989			−0.622752
$135$		0			0
$136$	−873.789	−	1513.45i	−0.550932	−	0.954243i
$137$	933.564	+	1616.98i	0.582188	+	1.00838i	0.995220	+	0.0976621i	$0.0311364\pi$
$137$	933.564	+	1616.98i	0.582188	+	1.00838i	−0.413032	+	0.910717i	$0.635530\pi$
$138$		0			0
$139$	−639.778			−0.390397			−0.195199	−	0.980764i	$-0.562535\pi$
$139$	−639.778			−0.390397			−0.195199	+	0.980764i	$0.562535\pi$
$140$		0			0
$141$		0			0
$142$	572.128	−	990.955i	0.338112	−	0.585627i
$143$	993.946	+	1721.56i	0.581244	+	1.00674i
$144$		0			0
$145$	475.792	−	824.095i	0.272499	−	0.471982i
$146$	621.446			0.352269
$147$		0			0
$148$	1454.99			0.808103
$149$	1568.27	−	2716.32i	0.862264	−	1.49348i	−0.00747495	−	0.999972i	$-0.502379\pi$
$149$	1568.27	−	2716.32i	0.862264	−	1.49348i	0.869739	−	0.493513i	$-0.164287\pi$
$150$		0			0
$151$	1360.68	+	2356.77i	0.733317	+	1.27014i	0.955458	+	0.295128i	$0.0953623\pi$
$151$	1360.68	+	2356.77i	0.733317	+	1.27014i	−0.222141	+	0.975015i	$0.571304\pi$
$152$	−224.638	+	389.085i	−0.119872	+	0.207625i
$153$		0			0
$154$		0			0
$155$	3547.20			1.83818
$156$		0			0
$157$	1439.87	+	2493.93i	0.731939	+	1.26776i	0.956053	+	0.293193i	$0.0947178\pi$
$157$	1439.87	+	2493.93i	0.731939	+	1.26776i	−0.224114	+	0.974563i	$0.571949\pi$
$158$	−231.511	−	400.989i	−0.116570	−	0.201905i
$159$		0			0
$160$	3414.22			1.68699
$161$		0			0
$162$		0			0
$163$	−323.071	+	559.576i	−0.155245	+	0.268892i	−0.933148	−	0.359492i	$-0.882950\pi$
$163$	−323.071	+	559.576i	−0.155245	+	0.268892i	0.777903	+	0.628384i	$0.216283\pi$
$164$	−553.271	−	958.293i	−0.263434	−	0.456281i
$165$		0			0
$166$	92.4093	−	160.058i	0.0432069	−	0.0748366i
$167$	3765.03			1.74459			0.872296	−	0.488979i	$-0.162630\pi$
$167$	3765.03			1.74459			0.872296	+	0.488979i	$0.162630\pi$
$168$		0			0
$169$	−1144.24			−0.520821
$170$	−1188.67	+	2058.83i	−0.536274	+	0.928854i
$171$		0			0
$172$	−59.7777	−	103.538i	−0.0265001	−	0.0458995i
$173$	1154.49	−	1999.64i	0.507366	−	0.878783i	−0.492598	−	0.870257i	$-0.663953\pi$
$173$	1154.49	−	1999.64i	0.507366	−	0.878783i	0.999964	−	0.00852600i	$-0.00271394\pi$
$174$		0			0
$175$		0			0
$176$	565.565			0.242222
$177$		0			0
$178$	−750.577	−	1300.04i	−0.316057	−	0.547427i
$179$	−1516.88	−	2627.31i	−0.633390	−	1.09706i	−0.986854	−	0.161616i	$-0.948329\pi$
$179$	−1516.88	−	2627.31i	−0.633390	−	1.09706i	0.353464	−	0.935448i	$-0.385004\pi$
$180$		0			0
$181$	4079.71			1.67537			0.837686	−	0.546152i	$-0.183908\pi$
$181$	4079.71			1.67537			0.837686	+	0.546152i	$0.183908\pi$
$182$		0			0
$183$		0			0
$184$	362.403	−	627.700i	0.145199	−	0.251493i
$185$	−2443.36	−	4232.03i	−0.971025	−	1.68186i
$186$		0			0
$187$	−2491.40	+	4315.23i	−0.974274	+	1.68749i
$188$	−1350.24			−0.523809
$189$		0			0
$190$	611.177			0.233365
$191$	438.554	−	759.599i	0.166140	−	0.287762i	−0.770920	−	0.636932i	$-0.780203\pi$
$191$	438.554	−	759.599i	0.166140	−	0.287762i	0.937059	+	0.349170i	$0.113536\pi$
$192$		0			0
$193$	729.356	+	1263.28i	0.272022	+	0.471155i	0.969379	−	0.245568i	$-0.0789744\pi$
$193$	729.356	+	1263.28i	0.272022	+	0.471155i	−0.697358	+	0.716723i	$0.745641\pi$
$194$	−96.1979	+	166.620i	−0.0356011	+	0.0616629i
$195$		0			0
$196$		0			0
$197$	−952.250			−0.344391			−0.172195	−	0.985063i	$-0.555086\pi$
$197$	−952.250			−0.344391			−0.172195	+	0.985063i	$0.555086\pi$
$198$		0			0
$199$	1671.11	+	2894.44i	0.595285	+	1.03106i	0.993507	+	0.113774i	$0.0362941\pi$
$199$	1671.11	+	2894.44i	0.595285	+	1.03106i	−0.398222	+	0.917289i	$0.630373\pi$
$200$	−2251.77	−	3900.18i	−0.796120	−	1.37892i
$201$		0			0
$202$	2047.11			0.713041
$203$		0			0
$204$		0			0
$205$	−1858.22	+	3218.52i	−0.633090	+	1.09654i
$206$	−424.554	−	735.349i	−0.143593	−	0.248710i
$207$		0			0
$208$	149.757	−	259.387i	0.0499221	−	0.0864677i
$209$	1281.00			0.423966
$210$		0			0
$211$	1439.27			0.469589			0.234794	−	0.972045i	$-0.424558\pi$
$211$	1439.27			0.469589			0.234794	+	0.972045i	$0.424558\pi$
$212$	383.485	−	664.216i	0.124235	−	0.215182i
$213$		0			0
$214$	106.552	+	184.553i	0.0340361	+	0.0589522i
$215$	−200.770	+	347.743i	−0.0636855	+	0.110306i
$216$		0			0
$217$		0			0
$218$	348.007			0.108119
$219$		0			0
$220$	−3051.74	−	5285.77i	−0.935220	−	1.61985i
$221$	1319.41	+	2285.28i	0.401597	+	0.695587i
$222$		0			0
$223$	−1009.86			−0.303253			−0.151626	−	0.988438i	$-0.548451\pi$
$223$	−1009.86			−0.303253			−0.151626	+	0.988438i	$0.548451\pi$
$224$		0			0
$225$		0			0
$226$	−1602.92	+	2776.34i	−0.471790	+	0.817165i
$227$	1474.30	+	2553.57i	0.431070	+	0.746635i	0.996966	−	0.0778419i	$-0.0248029\pi$
$227$	1474.30	+	2553.57i	0.431070	+	0.746635i	−0.565896	+	0.824477i	$0.691470\pi$
$228$		0			0
$229$	−2019.42	+	3497.74i	−0.582739	+	1.00933i	0.412414	+	0.910997i	$0.364686\pi$
$229$	−2019.42	+	3497.74i	−0.582739	+	1.00933i	−0.995153	+	0.0983374i	$0.968648\pi$
$230$	−985.995			−0.282672
$231$		0			0
$232$	1117.85			0.316339
$233$	1497.90	−	2594.44i	0.421162	−	0.729473i	−0.574892	−	0.818230i	$-0.694956\pi$
$233$	1497.90	−	2594.44i	0.421162	−	0.729473i	0.996053	+	0.0887561i	$0.0282892\pi$
$234$		0			0
$235$	2267.45	+	3927.34i	0.629413	+	1.09018i
$236$	603.081	−	1044.57i	0.166344	−	0.288117i
$237$		0			0
$238$		0			0
$239$	1810.28			0.489948			0.244974	−	0.969530i	$-0.421221\pi$
$239$	1810.28			0.489948			0.244974	+	0.969530i	$0.421221\pi$
$240$		0			0
$241$	−1874.71	−	3247.10i	−0.501083	−	0.867900i	−0.999999	−	0.00125048i	$-0.999602\pi$
$241$	−1874.71	−	3247.10i	−0.501083	−	0.867900i	0.498917	−	0.866650i	$-0.333731\pi$
$242$	1935.79	+	3352.88i	0.514203	+	0.890625i
$243$		0			0
$244$	3553.80			0.932414
$245$		0			0
$246$		0			0
$247$	339.200	−	587.512i	0.0873797	−	0.151346i
$248$	2083.50	+	3608.74i	0.533478	+	0.924012i
$249$		0			0
$250$	−1236.27	+	2141.28i	−0.312754	+	0.541706i
$251$	−2706.96			−0.680724			−0.340362	−	0.940295i	$-0.610550\pi$
$251$	−2706.96			−0.680724			−0.340362	+	0.940295i	$0.610550\pi$
$252$		0			0
$253$	−2066.61			−0.513544
$254$	1309.54	−	2268.20i	0.323496	−	0.560312i
$255$		0			0
$256$	1804.29	+	3125.13i	0.440502	+	0.762971i
$257$	−2687.64	+	4655.13i	−0.652337	+	1.12988i	0.330218	+	0.943905i	$0.392878\pi$
$257$	−2687.64	+	4655.13i	−0.652337	+	1.12988i	−0.982554	+	0.185975i	$0.940456\pi$
$258$		0			0
$259$		0			0
$260$	−3232.31			−0.770998
$261$		0			0
$262$	−73.3116	−	126.979i	−0.0172870	−	0.0299420i
$263$	2623.28	+	4543.66i	0.615051	+	1.06530i	0.990376	+	0.138406i	$0.0441979\pi$
$263$	2623.28	+	4543.66i	0.615051	+	1.06530i	−0.375324	+	0.926893i	$0.622469\pi$
$264$		0			0
$265$	−2575.95			−0.597129
$266$		0			0
$267$		0			0
$268$	1646.06	−	2851.06i	0.375184	−	0.649837i
$269$	−1506.66	−	2609.61i	−0.341496	−	0.591489i	0.643214	−	0.765686i	$-0.277600\pi$
$269$	−1506.66	−	2609.61i	−0.341496	−	0.591489i	−0.984711	+	0.174197i	$0.944267\pi$
$270$		0			0
$271$	3448.62	−	5973.19i	0.773022	−	1.33891i	−0.162877	−	0.986646i	$-0.552077\pi$
$271$	3448.62	−	5973.19i	0.773022	−	1.33891i	0.935899	−	0.352267i	$-0.114589\pi$
$272$	750.756			0.167358
$273$		0			0
$274$	2983.77			0.657869
$275$	−6420.37	+	11120.4i	−1.40787	+	2.43850i
$276$		0			0
$277$	−1659.30	−	2874.00i	−0.359920	−	0.623400i	0.628027	−	0.778191i	$-0.283863\pi$
$277$	−1659.30	−	2874.00i	−0.359920	−	0.623400i	−0.987947	+	0.154792i	$0.950529\pi$
$278$	−511.200	+	885.424i	−0.110287	+	0.191022i
$279$		0			0
$280$		0			0
$281$	−6274.14			−1.33197			−0.665986	−	0.745964i	$-0.731989\pi$
$281$	−6274.14			−1.33197			−0.665986	+	0.745964i	$0.731989\pi$
$282$		0			0
$283$	3886.24	+	6731.16i	0.816300	+	1.41387i	0.908391	+	0.418122i	$0.137311\pi$
$283$	3886.24	+	6731.16i	0.816300	+	1.41387i	−0.0920914	+	0.995751i	$0.529355\pi$
$284$	1949.83	+	3377.21i	0.407399	+	0.705635i
$285$		0			0
$286$	3176.76			0.656803
$287$		0			0
$288$		0			0
$289$	−850.695	+	1473.45i	−0.173152	+	0.299908i
$290$	−760.341	−	1316.95i	−0.153961	−	0.266669i
$291$		0			0
$292$	−1058.95	+	1834.16i	−0.212228	+	0.367590i
$293$	−854.897			−0.170456			−0.0852280	−	0.996361i	$-0.527162\pi$
$293$	−854.897			−0.170456			−0.0852280	+	0.996361i	$0.527162\pi$
$294$		0			0
$295$	−4051.02			−0.799523
$296$	2870.29	−	4971.49i	0.563623	−	0.976223i
$297$		0			0
$298$	−2506.17	−	4340.82i	−0.487177	−	0.843815i
$299$	−547.222	+	947.817i	−0.105842	+	0.183323i
$300$		0			0
$301$		0			0
$302$	4348.89			0.828645
$303$		0			0
$304$	−96.5041	−	167.150i	−0.0182069	−	0.0315352i
$305$	−5967.90	−	10336.7i	−1.12040	−	1.94058i
$306$		0			0
$307$	−2550.68			−0.474185			−0.237092	−	0.971487i	$-0.576194\pi$
$307$	−2550.68			−0.474185			−0.237092	+	0.971487i	$0.576194\pi$
$308$		0			0
$309$		0			0
$310$	2834.31	−	4909.17i	0.519284	−	0.899427i
$311$	3740.25	+	6478.31i	0.681962	+	1.18119i	0.974381	+	0.224903i	$0.0722064\pi$
$311$	3740.25	+	6478.31i	0.681962	+	1.18119i	−0.292419	+	0.956290i	$0.594460\pi$
$312$		0			0
$313$	3.12392	−	5.41079i	0.000564135	−	0.000977111i	−0.865743	−	0.500488i	$-0.833154\pi$
$313$	3.12392	−	5.41079i	0.000564135	−	0.000977111i	0.866307	+	0.499511i	$0.166487\pi$
$314$	4601.99			0.827088
$315$		0			0
$316$	1578.00			0.280915
$317$	−482.902	+	836.410i	−0.0855598	+	0.148194i	−0.905630	−	0.424070i	$-0.860601\pi$
$317$	−482.902	+	836.410i	−0.0855598	+	0.148194i	0.820070	+	0.572263i	$0.193935\pi$
$318$		0			0
$319$	−1593.64	−	2760.27i	−0.279708	−	0.484469i
$320$	2052.64	−	3555.28i	0.358582	−	0.621083i
$321$		0			0
$322$		0			0
$323$	1700.46			0.292929
$324$		0			0
$325$	3400.13	+	5889.20i	0.580324	+	1.00515i
$326$	516.285	+	894.232i	0.0877129	+	0.151923i
$327$		0			0
$328$	−4365.80			−0.734942
$329$		0			0
$330$		0			0
$331$	−3355.10	+	5811.20i	−0.557139	+	0.964992i	0.440595	+	0.897706i	$0.354767\pi$
$331$	−3355.10	+	5811.20i	−0.557139	+	0.964992i	−0.997734	+	0.0672865i	$0.978566\pi$
$332$	314.934	+	545.482i	0.0520610	+	0.0901723i
$333$		0			0
$334$	3008.36	−	5210.64i	0.492845	−	0.853633i
$335$	−11056.9			−1.80330
$336$		0			0
$337$	−605.546			−0.0978819			−0.0489409	−	0.998802i	$-0.515585\pi$
$337$	−605.546			−0.0978819			−0.0489409	+	0.998802i	$0.515585\pi$
$338$	−914.281	+	1583.58i	−0.147131	+	0.254839i
$339$		0			0
$340$	−4051.02	−	7016.57i	−0.646168	−	1.11920i
$341$	5940.61	−	10289.4i	0.943408	−	1.63403i
$342$		0			0
$343$		0			0
$344$	−471.700			−0.0739313
$345$		0			0
$346$	−1844.94	−	3195.53i	−0.286660	−	0.496510i
$347$	−3469.08	−	6008.62i	−0.536686	−	0.929567i	−0.999080	−	0.0428923i	$-0.986343\pi$
$347$	−3469.08	−	6008.62i	−0.536686	−	0.929567i	0.462394	−	0.886675i	$-0.346991\pi$
$348$		0			0
$349$	−10368.9			−1.59035			−0.795176	−	0.606378i	$-0.792622\pi$
$349$	−10368.9			−1.59035			−0.795176	+	0.606378i	$0.792622\pi$
$350$		0			0
$351$		0			0
$352$	5717.90	−	9903.69i	0.865809	−	1.49963i
$353$	−2940.88	−	5093.75i	−0.443420	−	0.768026i	0.554521	−	0.832170i	$-0.312902\pi$
$353$	−2940.88	−	5093.75i	−0.443420	−	0.768026i	−0.997941	+	0.0641440i	$0.979568\pi$
$354$		0			0
$355$	6548.70	−	11342.7i	0.979068	−	1.69580i
$356$	5115.98			0.761647
$357$		0			0
$358$	−4848.11			−0.715728
$359$	−294.634	+	510.322i	−0.0433153	+	0.0750244i	−0.886870	−	0.462019i	$-0.847125\pi$
$359$	−294.634	+	510.322i	−0.0433153	+	0.0750244i	0.843555	+	0.537043i	$0.180459\pi$
$360$		0			0
$361$	3210.92	+	5561.47i	0.468132	+	0.810829i
$362$	3259.80	−	5646.14i	0.473291	−	0.819763i
$363$		0			0
$364$		0			0
$365$	7113.21			1.02006
$366$		0			0
$367$	−1774.36	−	3073.28i	−0.252373	−	0.437122i	0.711806	−	0.702376i	$-0.247878\pi$
$367$	−1774.36	−	3073.28i	−0.252373	−	0.437122i	−0.964179	+	0.265254i	$0.914544\pi$
$368$	155.687	+	269.658i	0.0220537	+	0.0381982i
$369$		0			0
$370$	−7809.25			−1.09725
$371$		0			0
$372$		0			0
$373$	790.667	−	1369.47i	0.109756	−	0.190104i	−0.805915	−	0.592031i	$-0.798326\pi$
$373$	790.667	−	1369.47i	0.109756	−	0.190104i	0.915672	+	0.401927i	$0.131660\pi$
$374$	3981.39	+	6895.97i	0.550462	+	0.953429i
$375$		0			0
$376$	−2663.64	+	4613.56i	−0.365337	+	0.632783i
$377$	−1687.94			−0.230592
$378$		0			0
$379$	3057.01			0.414322			0.207161	−	0.978307i	$-0.433578\pi$
$379$	3057.01			0.414322			0.207161	+	0.978307i	$0.433578\pi$
$380$	−1041.46	+	1803.85i	−0.140594	+	0.243515i
$381$		0			0
$382$	−700.834	−	1213.88i	−0.0938685	−	0.162585i
$383$	−5289.87	+	9162.33i	−0.705744	+	1.22238i	0.260678	+	0.965426i	$0.416054\pi$
$383$	−5289.87	+	9162.33i	−0.705744	+	1.22238i	−0.966422	+	0.256959i	$0.917280\pi$
$384$		0			0
$385$		0			0
$386$	2331.10			0.307383
$387$		0			0
$388$	−327.846	−	567.845i	−0.0428965	−	0.0742989i
$389$	3696.65	+	6402.78i	0.481819	+	0.834534i	0.999782	−	0.0208684i	$-0.00664310\pi$
$389$	3696.65	+	6402.78i	0.481819	+	0.834534i	−0.517964	+	0.855403i	$0.673310\pi$
$390$		0			0
$391$	−2743.31			−0.354821
$392$		0			0
$393$		0			0
$394$	−760.874	+	1317.87i	−0.0972900	+	0.168511i
$395$	−2649.93	−	4589.81i	−0.337550	−	0.584654i
$396$		0			0
$397$	889.086	−	1539.94i	0.112398	−	0.194679i	−0.804339	−	0.594171i	$-0.797480\pi$
$397$	889.086	−	1539.94i	0.112398	−	0.194679i	0.916737	+	0.399492i	$0.130814\pi$
$398$	5341.04			0.672669
$399$		0			0
$400$	1934.71			0.241839
$401$	73.8031	−	127.831i	0.00919090	−	0.0159191i	−0.861393	−	0.507938i	$-0.830408\pi$
$401$	73.8031	−	127.831i	0.00919090	−	0.0159191i	0.870584	+	0.492019i	$0.163741\pi$
$402$		0			0
$403$	−3146.06	−	5449.13i	−0.388874	−	0.673550i
$404$	−3488.31	+	6041.94i	−0.429579	+	0.744053i
$405$		0			0
$406$		0			0
$407$	−16367.9			−1.99343
$408$		0			0
$409$	−1080.03	−	1870.66i	−0.130572	−	0.226157i	0.793325	−	0.608798i	$-0.208348\pi$
$409$	−1080.03	−	1870.66i	−0.130572	−	0.226157i	−0.923897	+	0.382641i	$0.875015\pi$
$410$	2969.53	+	5143.37i	0.357694	+	0.619544i
$411$		0			0
$412$	2893.79			0.346036
$413$		0			0
$414$		0			0
$415$	1057.74	−	1832.05i	0.125114	−	0.216704i
$416$	−3028.11	−	5244.84i	−0.356888	−	0.618148i
$417$		0			0
$418$	1023.56	−	1772.85i	0.119770	−	0.207447i
$419$	13491.0			1.57298			0.786488	−	0.617605i	$-0.211897\pi$
$419$	13491.0			1.57298			0.786488	+	0.617605i	$0.211897\pi$
$420$		0			0
$421$	−14146.7			−1.63769			−0.818847	−	0.574012i	$-0.805386\pi$
$421$	−14146.7			−1.63769			−0.818847	+	0.574012i	$0.805386\pi$
$422$	1150.01	−	1991.88i	0.132658	−	0.229771i
$423$		0			0
$424$	−1513.02	−	2620.63i	−0.173299	−	0.300163i
$425$	−8522.69	+	14761.7i	−0.972732	+	1.68482i
$426$		0			0
$427$		0			0
$428$	−726.262			−0.0820215
$429$		0			0
$430$	320.841	+	555.712i	0.0359821	+	0.0623229i
$431$	4544.26	+	7870.89i	0.507864	+	0.879646i	0.999959	+	0.00910411i	$0.00289797\pi$
$431$	4544.26	+	7870.89i	0.507864	+	0.879646i	−0.492095	+	0.870542i	$0.663769\pi$
$432$		0			0
$433$	−15461.2			−1.71597			−0.857986	−	0.513673i	$-0.828284\pi$
$433$	−15461.2			−1.71597			−0.857986	+	0.513673i	$0.828284\pi$
$434$		0			0
$435$		0			0
$436$	−593.009	+	1027.12i	−0.0651376	+	0.112822i
$437$	352.632	+	610.776i	0.0386010	+	0.0668590i
$438$		0			0
$439$	−891.091	+	1543.41i	−0.0968780	+	0.167798i	−0.910391	−	0.413749i	$-0.864219\pi$
$439$	−891.091	+	1543.41i	−0.0968780	+	0.167798i	0.813513	+	0.581547i	$0.197552\pi$
$440$	−24081.0			−2.60913
$441$		0			0
$442$	4216.97			0.453803
$443$	6712.36	−	11626.1i	0.719896	−	1.24690i	−0.241145	−	0.970489i	$-0.577523\pi$
$443$	6712.36	−	11626.1i	0.719896	−	1.24690i	0.961041	−	0.276407i	$-0.0891437\pi$
$444$		0			0
$445$	−8591.27	−	14880.5i	−0.915203	−	1.58518i
$446$	−806.907	+	1397.60i	−0.0856685	+	0.148382i
$447$		0			0
$448$		0			0
$449$	−418.639			−0.0440018			−0.0220009	−	0.999758i	$-0.507004\pi$
$449$	−418.639			−0.0440018			−0.0220009	+	0.999758i	$0.507004\pi$
$450$		0			0
$451$	6224.02	+	10780.3i	0.649839	+	1.12555i
$452$	−5462.80	−	9461.85i	−0.568470	−	0.984619i
$453$		0			0
$454$	4712.03			0.487107
$455$		0			0
$456$		0			0
$457$	354.205	−	613.501i	0.0362560	−	0.0627973i	−0.847328	−	0.531070i	$-0.821790\pi$
$457$	354.205	−	613.501i	0.0362560	−	0.0627973i	0.883584	+	0.468273i	$0.155123\pi$
$458$	3227.15	+	5589.59i	0.329246	+	0.570271i
$459$		0			0
$460$	1680.15	−	2910.11i	0.170299	−	0.294966i
$461$	8223.97			0.830865			0.415432	−	0.909624i	$-0.363630\pi$
$461$	8223.97			0.830865			0.415432	+	0.909624i	$0.363630\pi$
$462$		0			0
$463$	−9414.17			−0.944954			−0.472477	−	0.881343i	$-0.656640\pi$
$463$	−9414.17			−0.944954			−0.472477	+	0.881343i	$0.656640\pi$
$464$	−240.114	+	415.889i	−0.0240237	+	0.0416103i
$465$		0			0
$466$	−2393.73	−	4146.05i	−0.237955	−	0.412151i
$467$	5410.76	−	9371.72i	0.536146	−	0.928632i	−0.462961	−	0.886379i	$-0.653213\pi$
$467$	5410.76	−	9371.72i	0.536146	−	0.928632i	0.999107	−	0.0422535i	$-0.0134537\pi$
$468$		0			0
$469$		0			0
$470$	7247.02			0.711234
$471$		0			0
$472$	−2379.43	−	4121.29i	−0.232038	−	0.401902i
$473$	672.470	+	1164.75i	0.0653704	+	0.113225i
$474$		0			0
$475$	4382.11			0.423295
$476$		0			0
$477$		0			0
$478$	1446.47	−	2505.35i	0.138410	−	0.239733i
$479$	−4092.75	−	7088.85i	−0.390402	−	0.676196i	0.602100	−	0.798420i	$-0.294331\pi$
$479$	−4092.75	−	7088.85i	−0.390402	−	0.676196i	−0.992503	+	0.122224i	$0.960997\pi$
$480$		0			0
$481$	−4334.09	+	7506.87i	−0.410848	+	0.711609i
$482$	−5991.79			−0.566221
$483$		0			0
$484$	−13194.4			−1.23915
$485$	−1101.10	+	1907.17i	−0.103090	+	0.178557i
$486$		0			0
$487$	2001.58	+	3466.83i	0.186242	+	0.322581i	0.943994	−	0.329961i	$-0.107036\pi$
$487$	2001.58	+	3466.83i	0.186242	+	0.322581i	−0.757752	+	0.652543i	$0.773702\pi$
$488$	7010.67	−	12142.8i	0.650324	−	1.12639i
$489$		0			0
$490$		0			0
$491$	11180.8			1.02766			0.513831	−	0.857891i	$-0.328226\pi$
$491$	11180.8			1.02766			0.513831	+	0.857891i	$0.328226\pi$
$492$		0			0
$493$	−2115.47	−	3664.11i	−0.193258	−	0.334733i
$494$	−542.060	−	938.876i	−0.0493693	−	0.0855101i
$495$		0			0
$496$	−1790.14			−0.162056
$497$		0			0
$498$		0			0
$499$	1885.54	−	3265.85i	0.169155	−	0.292985i	−0.768968	−	0.639287i	$-0.779229\pi$
$499$	1885.54	−	3265.85i	0.169155	−	0.292985i	0.938123	+	0.346302i	$0.112563\pi$
$500$	−4213.24	−	7297.55i	−0.376844	−	0.652713i
$501$		0			0
$502$	−2162.93	+	3746.31i	−0.192304	+	0.333080i
$503$	13597.2			1.20531			0.602654	−	0.798003i	$-0.294110\pi$
$503$	13597.2			1.20531			0.602654	+	0.798003i	$0.294110\pi$
$504$		0			0
$505$	23431.7			2.06475
$506$	−1651.28	+	2860.09i	−0.145075	+	0.251278i
$507$		0			0
$508$	4462.97	+	7730.08i	0.389788	+	0.675132i
$509$	3680.38	−	6374.60i	0.320491	−	0.555106i	−0.660099	−	0.751179i	$-0.729485\pi$
$509$	3680.38	−	6374.60i	0.320491	−	0.555106i	0.980589	+	0.196073i	$0.0628188\pi$
$510$		0			0
$511$		0			0
$512$	−3309.87			−0.285698
$513$		0			0
$514$	4295.00	+	7439.16i	0.368569	+	0.638380i
$515$	−4859.54	−	8416.97i	−0.415800	−	0.720186i
$516$		0			0
$517$	15189.5			1.29213
$518$		0			0
$519$		0			0
$520$	−6376.46	+	11044.4i	−0.537743	+	0.931398i
$521$	6899.40	+	11950.1i	0.580169	+	1.00488i	0.995459	+	0.0951930i	$0.0303468\pi$
$521$	6899.40	+	11950.1i	0.580169	+	1.00488i	−0.415290	+	0.909689i	$0.636320\pi$
$522$		0			0
$523$	9423.58	−	16322.1i	0.787886	−	1.36466i	−0.139373	−	0.990240i	$-0.544509\pi$
$523$	9423.58	−	16322.1i	0.787886	−	1.36466i	0.927260	−	0.374419i	$-0.122158\pi$
$524$	499.697			0.0416591
$525$		0			0
$526$	8384.29			0.695005
$527$	7885.83	−	13658.7i	0.651826	−	1.12900i
$528$		0			0
$529$	5514.61	+	9551.58i	0.453243	+	0.785040i
$530$	−2058.25	+	3565.00i	−0.168688	+	0.292177i
$531$		0			0
$532$		0			0
$533$	6592.29			0.535730
$534$		0			0
$535$	1219.61	+	2112.43i	0.0985579	+	0.170707i
$536$	−6494.45	−	11248.7i	−0.523354	−	0.906475i
$537$		0			0
$538$	−4815.44			−0.385889
$539$		0			0
$540$		0			0
$541$	7234.77	−	12531.0i	0.574948	−	0.995839i	−0.421099	−	0.907015i	$-0.638356\pi$
$541$	7234.77	−	12531.0i	0.574948	−	0.995839i	0.996047	−	0.0888248i	$-0.0283111\pi$
$542$	−5511.09	−	9545.49i	−0.436756	−	0.756483i
$543$		0			0
$544$	7590.19	−	13146.6i	0.598211	−	1.03613i
$545$	3983.36			0.313080
$546$		0			0
$547$	5749.63			0.449427			0.224713	−	0.974425i	$-0.427855\pi$
$547$	5749.63			0.449427			0.224713	+	0.974425i	$0.427855\pi$
$548$	−5084.39	+	8806.43i	−0.396340	+	0.686482i
$549$		0			0
$550$	10260.1	+	17771.0i	0.795441	+	1.37774i
$551$	−543.857	+	941.988i	−0.0420492	+	0.0728313i
$552$		0			0
$553$		0			0
$554$	−5303.31			−0.406708
$555$		0			0
$556$	−1742.19	−	3017.55i	−0.132887	−	0.230167i
$557$	−2715.39	−	4703.19i	−0.206561	−	0.357775i	0.744068	−	0.668104i	$-0.232894\pi$
$557$	−2715.39	−	4703.19i	−0.206561	−	0.357775i	−0.950629	+	0.310330i	$0.899561\pi$
$558$		0			0
$559$	712.260			0.0538915
$560$		0			0
$561$		0			0
$562$	−5013.21	+	8683.14i	−0.376280	+	0.651737i
$563$	−12065.3	−	20897.8i	−0.903185	−	1.56436i	−0.823335	−	0.567556i	$-0.807889\pi$
$563$	−12065.3	−	20897.8i	−0.903185	−	1.56436i	−0.0798500	−	0.996807i	$-0.525444\pi$
$564$		0			0
$565$	−18347.4	+	31778.6i	−1.36616	+	2.36626i
$566$	12420.8			0.922415
$567$		0			0
$568$	15385.9			1.13658
$569$	−9024.27	+	15630.5i	−0.664880	+	1.15161i	0.314437	+	0.949278i	$0.398184\pi$
$569$	−9024.27	+	15630.5i	−0.664880	+	1.15161i	−0.979318	+	0.202328i	$0.935149\pi$
$570$		0			0
$571$	5637.42	+	9764.30i	0.413168	+	0.715628i	0.995234	−	0.0975136i	$-0.0310889\pi$
$571$	5637.42	+	9764.30i	0.413168	+	0.715628i	−0.582066	+	0.813141i	$0.697756\pi$
$572$	−5413.25	+	9376.02i	−0.395698	+	0.685369i
$573$		0			0
$574$		0			0
$575$	−7069.54			−0.512731
$576$		0			0
$577$	−12047.5	−	20866.8i	−0.869225	−	1.50554i	−0.862790	−	0.505562i	$-0.831285\pi$
$577$	−12047.5	−	20866.8i	−0.869225	−	1.50554i	−0.00643457	−	0.999979i	$-0.502048\pi$
$578$	1359.46	+	2354.65i	0.0978303	+	0.169447i
$579$		0			0
$580$	5182.53			0.371022
$581$		0			0
$582$		0			0
$583$	−4314.02	+	7472.10i	−0.306464	+	0.530811i
$584$	4178.05	+	7236.59i	0.296043	+	0.512761i
$585$		0			0
$586$	−683.086	+	1183.14i	−0.0481536	+	0.0834045i
$587$	−11438.9			−0.804315			−0.402157	−	0.915571i	$-0.631740\pi$
$587$	−11438.9			−0.804315			−0.402157	+	0.915571i	$0.631740\pi$
$588$		0			0
$589$	−4054.66			−0.283649
$590$	−3236.87	+	5606.43i	−0.225864	+	0.391208i
$591$		0			0
$592$	1233.07	+	2135.74i	0.0856063	+	0.148274i
$593$	−2087.22	+	3615.17i	−0.144539	+	0.250349i	−0.929201	−	0.369575i	$-0.879503\pi$
$593$	−2087.22	+	3615.17i	−0.144539	+	0.250349i	0.784662	+	0.619924i	$0.212837\pi$
$594$		0			0
$595$		0			0
$596$	17082.2			1.17402
$597$		0			0
$598$	874.491	+	1514.66i	0.0598003	+	0.103577i
$599$	5727.77	+	9920.79i	0.390702	+	0.676715i	0.992542	−	0.121901i	$-0.0388991\pi$
$599$	5727.77	+	9920.79i	0.390702	+	0.676715i	−0.601841	+	0.798616i	$0.705566\pi$
$600$		0			0
$601$	17539.2			1.19042			0.595208	−	0.803572i	$-0.297070\pi$
$601$	17539.2			1.19042			0.595208	+	0.803572i	$0.297070\pi$
$602$		0			0
$603$		0			0
$604$	−7410.59	+	12835.5i	−0.499226	+	0.864685i
$605$	22157.4	+	38377.8i	1.48897	+	2.57898i
$606$		0			0
$607$	1692.86	−	2932.12i	0.113198	−	0.196064i	−0.803860	−	0.594818i	$-0.797224\pi$
$607$	1692.86	−	2932.12i	0.113198	−	0.196064i	0.917058	+	0.398754i	$0.130557\pi$
$608$	−3902.65			−0.260318
$609$		0			0
$610$	−19074.1			−1.26604
$611$	4022.06	−	6966.41i	0.266309	−	0.461261i
$612$		0			0
$613$	−2135.94	−	3699.56i	−0.140734	−	0.243758i	0.787039	−	0.616903i	$-0.211613\pi$
$613$	−2135.94	−	3699.56i	−0.140734	−	0.243758i	−0.927773	+	0.373145i	$0.878279\pi$
$614$	−2038.06	+	3530.02i	−0.133957	+	0.232020i
$615$		0			0
$616$		0			0
$617$	−13123.9			−0.856321			−0.428160	−	0.903703i	$-0.640838\pi$
$617$	−13123.9			−0.856321			−0.428160	+	0.903703i	$0.640838\pi$
$618$		0			0
$619$	−946.969	−	1640.20i	−0.0614893	−	0.106503i	0.833642	−	0.552305i	$-0.186252\pi$
$619$	−946.969	−	1640.20i	−0.0614893	−	0.106503i	−0.895131	+	0.445803i	$0.852918\pi$
$620$	9659.43	+	16730.6i	0.625697	+	1.08374i
$621$		0			0
$622$	11954.3			0.770614
$623$		0			0
$624$		0			0
$625$	−1051.49	+	1821.23i	−0.0672952	+	0.116559i
$626$	−4.99219	−	8.64673i	−0.000318735	−	0.000552066i
$627$		0			0
$628$	−7841.87	+	13582.5i	−0.498288	+	0.863060i
$629$	−21727.5			−1.37731
$630$		0			0
$631$	20443.8			1.28979			0.644894	−	0.764272i	$-0.276902\pi$
$631$	20443.8			1.28979			0.644894	+	0.764272i	$0.276902\pi$
$632$	3112.95	−	5391.79i	0.195928	−	0.339357i
$633$		0			0
$634$	771.703	+	1336.63i	0.0483411	+	0.0837292i
$635$	14989.3	−	25962.3i	0.936745	−	1.62249i
$636$		0			0
$637$		0			0
$638$	−5093.46			−0.316069
$639$		0			0
$640$	10376.6	+	17972.9i	0.640895	+	1.11006i
$641$	9614.27	+	16652.4i	0.592419	+	1.02610i	0.993906	+	0.110235i	$0.0351604\pi$
$641$	9614.27	+	16652.4i	0.592419	+	1.02610i	−0.401486	+	0.915865i	$0.631506\pi$
$642$		0			0
$643$	18525.1			1.13617			0.568087	−	0.822969i	$-0.307684\pi$
$643$	18525.1			1.13617			0.568087	+	0.822969i	$0.307684\pi$
$644$		0			0
$645$		0			0
$646$	1358.71	−	2353.36i	0.0827522	−	0.143331i
$647$	−4011.20	−	6947.60i	−0.243735	−	0.422161i	0.718040	−	0.696001i	$-0.245039\pi$
$647$	−4011.20	−	6947.60i	−0.243735	−	0.422161i	−0.961775	+	0.273840i	$0.911706\pi$
$648$		0			0
$649$	−6784.36	+	11750.9i	−0.410338	+	0.710726i
$650$	10867.2			0.655764
$651$		0			0
$652$	−3519.03			−0.211374
$653$	1025.85	−	1776.82i	0.0614769	−	0.106481i	−0.833649	−	0.552295i	$-0.813752\pi$
$653$	1025.85	−	1776.82i	0.0614769	−	0.106481i	0.895126	+	0.445814i	$0.147086\pi$
$654$		0			0
$655$	−839.141	−	1453.43i	−0.0500579	−	0.0867029i
$656$	937.770	−	1624.26i	0.0558136	−	0.0966721i
$657$		0			0
$658$		0			0
$659$	−14765.2			−0.872792			−0.436396	−	0.899755i	$-0.643745\pi$
$659$	−14765.2			−0.872792			−0.436396	+	0.899755i	$0.643745\pi$
$660$		0			0
$661$	323.532	+	560.374i	0.0190377	+	0.0329743i	0.875387	−	0.483422i	$-0.160606\pi$
$661$	323.532	+	560.374i	0.0190377	+	0.0329743i	−0.856350	+	0.516397i	$0.827273\pi$
$662$	5361.63	+	9286.62i	0.314782	+	0.545218i
$663$		0			0
$664$	2485.11			0.145243
$665$		0			0
$666$		0			0
$667$	877.390	−	1519.68i	0.0509335	−	0.0882195i
$668$	10252.6	+	17758.0i	0.593840	+	1.02856i
$669$		0			0
$670$	−8834.78	+	15302.3i	−0.509429	+	0.882357i
$671$	−39978.5			−2.30008
$672$		0			0
$673$	−22596.6			−1.29426			−0.647130	−	0.762380i	$-0.724031\pi$
$673$	−22596.6			−1.29426			−0.647130	+	0.762380i	$0.724031\pi$
$674$	−483.848	+	838.049i	−0.0276515	+	0.0478938i
$675$		0			0
$676$	−3115.90	−	5396.90i	−0.177282	−	0.307061i
$677$	−12602.1	+	21827.5i	−0.715420	+	1.23914i	0.247377	+	0.968919i	$0.420431\pi$
$677$	−12602.1	+	21827.5i	−0.715420	+	1.23914i	−0.962797	+	0.270225i	$0.912902\pi$
$678$		0			0
$679$		0			0
$680$	−31966.2			−1.80272
$681$		0			0
$682$	−9493.42	−	16443.1i	−0.533023	−	0.923223i
$683$	−8510.27	−	14740.2i	−0.476774	−	0.825796i	0.522872	−	0.852411i	$-0.324860\pi$
$683$	−8510.27	−	14740.2i	−0.476774	−	0.825796i	−0.999646	+	0.0266151i	$0.991527\pi$
$684$		0			0
$685$	34152.9			1.90499
$686$		0			0
$687$		0			0
$688$	101.321	−	175.493i	0.00561456	−	0.00972470i
$689$	2284.64	+	3957.11i	0.126325	+	0.218801i
$690$		0			0
$691$	−9645.26	+	16706.1i	−0.531003	+	0.919724i	0.468342	+	0.883547i	$0.344851\pi$
$691$	−9645.26	+	16706.1i	−0.531003	+	0.919724i	−0.999345	+	0.0361772i	$0.988482\pi$
$692$	12575.2			0.690806
$693$		0			0
$694$	−11087.6			−0.606452
$695$	−5851.31	+	10134.8i	−0.319356	+	0.553142i
$696$		0			0
$697$	8262.04	+	14310.3i	0.448991	+	0.777676i
$698$	−8285.01	+	14350.1i	−0.449273	+	0.778163i
$699$		0			0
$700$		0			0
$701$	28511.4			1.53618			0.768088	−	0.640345i	$-0.221208\pi$
$701$	28511.4			1.53618			0.768088	+	0.640345i	$0.221208\pi$
$702$		0			0
$703$	2792.90	+	4837.45i	0.149838	+	0.259528i
$704$	−6875.25	−	11908.3i	−0.368069	−	0.637515i
$705$		0			0
$706$	−9399.37			−0.501062
$707$		0			0
$708$		0			0
$709$	−14213.3	+	24618.1i	−0.752877	+	1.30402i	0.193546	+	0.981091i	$0.438001\pi$
$709$	−14213.3	+	24618.1i	−0.752877	+	1.30402i	−0.946423	+	0.322930i	$0.895332\pi$
$710$	−10465.2	−	18126.2i	−0.553171	−	0.958120i
$711$		0			0
$712$	10092.4	−	17480.6i	0.531221	−	0.920102i
$713$	6541.27			0.343580
$714$		0			0
$715$	36361.9			1.90190
$716$	8261.26	−	14308.9i	0.431198	−	0.746857i
$717$		0			0
$718$	470.842	+	815.522i	0.0244731	+	0.0423886i
$719$	−10881.7	+	18847.6i	−0.564420	+	0.977603i	0.432684	+	0.901546i	$0.357567\pi$
$719$	−10881.7	+	18847.6i	−0.564420	+	0.977603i	−0.997103	+	0.0760577i	$0.975767\pi$
$720$		0			0
$721$		0			0
$722$	10262.4			0.528987
$723$		0			0
$724$	11109.5	+	19242.2i	0.570278	+	0.987750i
$725$	−5451.61	−	9442.47i	−0.279266	−	0.483703i
$726$		0			0
$727$	13422.8			0.684763			0.342382	−	0.939561i	$-0.388766\pi$
$727$	13422.8			0.684763			0.342382	+	0.939561i	$0.388766\pi$
$728$		0			0
$729$		0			0
$730$	5683.65	−	9844.36i	0.288166	−	0.499118i
$731$	892.666	+	1546.14i	0.0451661	+	0.0782301i
$732$		0			0
$733$	2279.76	−	3948.66i	0.114877	−	0.198973i	−0.802854	−	0.596176i	$-0.796686\pi$
$733$	2279.76	−	3948.66i	0.114877	−	0.198973i	0.917731	+	0.397204i	$0.130019\pi$
$734$	−5671.04			−0.285180
$735$		0			0
$736$	6296.04			0.315319
$737$	−18517.4	+	32073.0i	−0.925503	+	1.60302i
$738$		0			0
$739$	18332.7	+	31753.2i	0.912557	+	1.58059i	0.810439	+	0.585823i	$0.199228\pi$
$739$	18332.7	+	31753.2i	0.912557	+	1.58059i	0.102118	+	0.994772i	$0.467438\pi$
$740$	13307.1	−	23048.6i	0.661052	−	1.14498i
$741$		0			0
$742$		0			0
$743$	−10321.3			−0.509625			−0.254813	−	0.966990i	$-0.582014\pi$
$743$	−10321.3			−0.509625			−0.254813	+	0.966990i	$0.582014\pi$
$744$		0			0
$745$	−28686.2	−	49686.0i	−1.41071	−	2.44343i
$746$	−1263.53	−	2188.50i	−0.0620121	−	0.107408i
$747$		0			0
$748$	−27137.4			−1.32653
$749$		0			0
$750$		0			0
$751$	13339.0	−	23103.9i	0.648134	−	1.12260i	−0.335434	−	0.942064i	$-0.608883\pi$
$751$	13339.0	−	23103.9i	0.648134	−	1.12260i	0.983568	−	0.180537i	$-0.0577836\pi$
$752$	−1144.30	−	1981.98i	−0.0554896	−	0.0961107i
$753$		0			0
$754$	−1348.71	+	2336.03i	−0.0651421	+	0.112829i
$755$	49778.4			2.39950
$756$		0			0
$757$	−11630.8			−0.558425			−0.279212	−	0.960229i	$-0.590073\pi$
$757$	−11630.8			−0.558425			−0.279212	+	0.960229i	$0.590073\pi$
$758$	2442.63	−	4230.77i	0.117045	−	0.202729i
$759$		0			0
$760$	4109.01	+	7117.02i	0.196118	+	0.339686i
$761$	18045.8	−	31256.3i	0.859607	−	1.48888i	−0.0126976	−	0.999919i	$-0.504042\pi$
$761$	18045.8	−	31256.3i	0.859607	−	1.48888i	0.872304	−	0.488963i	$-0.162625\pi$
$762$		0			0
$763$		0			0
$764$	4776.93			0.226208
$765$		0			0
$766$	8453.51	+	14641.9i	0.398744	+	0.690644i
$767$	3592.89	+	6223.07i	0.169142	+	0.292962i
$768$		0			0
$769$	−33089.3			−1.55167			−0.775833	−	0.630938i	$-0.782670\pi$
$769$	−33089.3			−1.55167			−0.775833	+	0.630938i	$0.782670\pi$
$770$		0			0
$771$		0			0
$772$	−3972.23	+	6880.11i	−0.185186	+	0.320752i
$773$	−15495.4	−	26838.8i	−0.720997	−	1.24880i	−0.960601	−	0.277933i	$-0.910351\pi$
$773$	−15495.4	−	26838.8i	−0.720997	−	1.24880i	0.239603	−	0.970871i	$-0.422983\pi$
$774$		0			0
$775$	20321.9	−	35198.6i	0.941915	−	1.63144i
$776$	−2587.00			−0.119675
$777$		0			0
$778$	11814.9			0.544453
$779$	2124.05	−	3678.96i	0.0976917	−	0.169207i
$780$		0			0
$781$	−21934.6	−	37991.9i	−1.00497	−	1.74066i
$782$	−2191.98	+	3796.62i	−0.100236	+	0.173615i
$783$		0			0
$784$		0			0
$785$	52675.4			2.39499
$786$		0			0
$787$	−12710.6	−	22015.4i	−0.575711	−	0.997161i	−0.995964	−	0.0897537i	$-0.971392\pi$
$787$	−12710.6	−	22015.4i	−0.575711	−	0.997161i	0.420253	−	0.907407i	$-0.361941\pi$
$788$	−2593.08	−	4491.35i	−0.117227	−	0.203043i
$789$		0			0
$790$	−8469.46			−0.381430
$791$		0			0
$792$		0			0
$793$	−10586.0	+	18335.5i	−0.474048	+	0.821075i
$794$	−1420.81	−	2460.91i	−0.0635045	−	0.109993i
$795$		0			0
$796$	−9101.22	+	15763.8i	−0.405257	+	0.701925i
$797$	20283.3			0.901470			0.450735	−	0.892658i	$-0.351162\pi$
$797$	20283.3			0.901470			0.450735	+	0.892658i	$0.351162\pi$
$798$		0			0
$799$	20163.2			0.892768
$800$	19560.0	−	33879.0i	0.864439	−	1.49725i
$801$		0			0
$802$	−117.941	−	204.281i	−0.00519284	−	0.00899426i
$803$	11912.7	−	20633.4i	0.523524	−	0.906771i
$804$		0			0
$805$		0			0
$806$	−10055.1			−0.439426
$807$		0			0
$808$	13763.0	+	23838.2i	0.599232	+	1.03790i
$809$	−8215.67	−	14230.0i	−0.357043	−	0.618416i	0.630423	−	0.776252i	$-0.282882\pi$
$809$	−8215.67	−	14230.0i	−0.357043	−	0.618416i	−0.987465	+	0.157836i	$0.949548\pi$
$810$		0			0
$811$	−6371.81			−0.275887			−0.137944	−	0.990440i	$-0.544049\pi$
$811$	−6371.81			−0.275887			−0.137944	+	0.990440i	$0.544049\pi$
$812$		0			0
$813$		0			0
$814$	−13078.4	+	22652.4i	−0.563142	+	0.975390i
$815$	5909.52	+	10235.6i	0.253989	+	0.439922i
$816$		0			0
$817$	229.491	−	397.490i	0.00982727	−	0.0170213i
$818$	−3451.88			−0.147545
$819$		0			0
$820$	−20240.5			−0.861987
$821$	2612.24	−	4524.54i	0.111045	−	0.192335i	−0.805147	−	0.593075i	$-0.797914\pi$
$821$	2612.24	−	4524.54i	0.111045	−	0.192335i	0.916192	+	0.400740i	$0.131247\pi$
$822$		0			0
$823$	−1856.55	−	3215.64i	−0.0786333	−	0.136197i	0.824027	−	0.566550i	$-0.191722\pi$
$823$	−1856.55	−	3215.64i	−0.0786333	−	0.136197i	−0.902660	+	0.430353i	$0.858389\pi$
$824$	5708.65	−	9887.67i	0.241347	−	0.418026i
$825$		0			0
$826$		0			0
$827$	10202.6			0.428996			0.214498	−	0.976724i	$-0.431188\pi$
$827$	10202.6			0.428996			0.214498	+	0.976724i	$0.431188\pi$
$828$		0			0
$829$	12497.6	+	21646.5i	0.523594	+	0.906891i	0.999623	+	0.0274616i	$0.00874239\pi$
$829$	12497.6	+	21646.5i	0.523594	+	0.906891i	−0.476029	+	0.879430i	$0.657924\pi$
$830$	−1690.32	−	2927.72i	−0.0706891	−	0.122437i
$831$		0			0
$832$	−7282.06			−0.303437
$833$		0			0
$834$		0			0
$835$	34434.4	−	59642.1i	1.42713	−	2.47186i
$836$	3488.31	+	6041.94i	0.144313	+	0.249958i
$837$		0			0
$838$	10779.7	−	18670.9i	0.444364	−	0.769661i
$839$	−31173.6			−1.28275			−0.641377	−	0.767226i	$-0.721637\pi$
$839$	−31173.6			−1.28275			−0.641377	+	0.767226i	$0.721637\pi$
$840$		0			0
$841$	−21682.6			−0.889033
$842$	−11303.6	+	19578.4i	−0.462646	+	0.801327i
$843$		0			0
$844$	3919.29	+	6788.40i	0.159843	+	0.276856i
$845$	−10465.1	+	18126.0i	−0.426046	+	0.737934i
$846$		0			0
$847$		0			0
$848$	1299.98			0.0526434
$849$		0			0
$850$	13619.7	+	23590.1i	0.549591	+	0.951920i
$851$	−4505.72	−	7804.13i	−0.181497	−	0.314362i
$852$		0			0
$853$	25280.7			1.01477			0.507383	−	0.861721i	$-0.330613\pi$
$853$	25280.7			1.01477			0.507383	+	0.861721i	$0.330613\pi$
$854$		0			0
$855$		0			0
$856$	−1432.72	+	2481.54i	−0.0572070	+	0.0990855i
$857$	−13705.4	−	23738.4i	−0.546285	−	0.946194i	−0.998525	−	0.0542972i	$-0.982708\pi$
$857$	−13705.4	−	23738.4i	−0.546285	−	0.946194i	0.452240	−	0.891896i	$-0.350625\pi$
$858$		0			0
$859$	12279.4	−	21268.6i	0.487740	−	0.844790i	−0.512161	−	0.858890i	$-0.671155\pi$
$859$	12279.4	−	21268.6i	0.487740	−	0.844790i	0.999901	+	0.0140994i	$0.00448813\pi$
$860$	−2186.87			−0.0867113
$861$		0			0
$862$	14523.9			0.573883
$863$	3574.18	−	6190.66i	0.140981	−	0.244186i	−0.786885	−	0.617099i	$-0.788308\pi$
$863$	3574.18	−	6190.66i	0.140981	−	0.244186i	0.927866	+	0.372913i	$0.121641\pi$
$864$		0			0
$865$	−21117.6	−	36576.7i	−0.830080	−	1.43774i
$866$	−12353.9	+	21397.6i	−0.484760	+	0.839629i
$867$		0			0
$868$		0			0
$869$	−17751.7			−0.692962
$870$		0			0
$871$	9806.52	+	16985.4i	0.381494	+	0.660767i
$872$	2339.69	+	4052.46i	0.0908621	+	0.157378i
$873$		0			0
$874$	1127.05			0.0436190
$875$		0			0
$876$		0			0
$877$	14109.2	−	24437.9i	0.543256	−	0.940946i	−0.455459	−	0.890257i	$-0.650525\pi$
$877$	14109.2	−	24437.9i	0.543256	−	0.940946i	0.998714	−	0.0506895i	$-0.0161419\pi$
$878$	1424.01	+	2466.46i	0.0547359	+	0.0948053i
$879$		0			0
$880$	5172.57	−	8959.15i	0.198145	−	0.343197i
$881$	−7431.50			−0.284192			−0.142096	−	0.989853i	$-0.545384\pi$
$881$	−7431.50			−0.284192			−0.142096	+	0.989853i	$0.545384\pi$
$882$		0			0
$883$	4937.77			0.188187			0.0940936	−	0.995563i	$-0.470005\pi$
$883$	4937.77			0.188187			0.0940936	+	0.995563i	$0.470005\pi$
$884$	−7185.79	+	12446.1i	−0.273398	+	0.473540i
$885$		0			0
$886$	−10726.7	−	18579.2i	−0.406739	−	0.704493i
$887$	−20986.8	+	36350.3i	−0.794441	+	1.37601i	0.128753	+	0.991677i	$0.458903\pi$
$887$	−20986.8	+	36350.3i	−0.794441	+	1.37601i	−0.923194	+	0.384335i	$0.874431\pi$
$888$		0			0
$889$		0			0
$890$	−27458.6			−1.03417
$891$		0			0
$892$	−2749.97	−	4763.08i	−0.103224	−	0.178789i
$893$	−2591.83	−	4489.17i	−0.0971245	−	0.168224i
$894$		0			0
$895$	−55492.5			−2.07253
$896$		0			0
$897$		0			0
$898$	−334.504	+	579.378i	−0.0124305	+	0.0215302i
$899$	5044.24	+	8736.88i	0.187135	+	0.324128i
$900$		0			0
$901$	−5726.62	+	9918.80i	−0.211744	+	0.366751i
$902$	19892.6			0.734315
$903$		0			0
$904$	−43106.4			−1.58595
$905$	37312.4	−	64626.9i	1.37050	−	2.37378i
$906$		0			0
$907$	−20712.1	−	35874.4i	−0.758252	−	1.31333i	−0.943741	−	0.330685i	$-0.892720\pi$
$907$	−20712.1	−	35874.4i	−0.758252	−	1.31333i	0.185489	−	0.982646i	$-0.440613\pi$
$908$	−8029.37	+	13907.3i	−0.293463	+	0.508292i
$909$		0			0
$910$		0			0
$911$	−40072.0			−1.45735			−0.728675	−	0.684860i	$-0.759864\pi$
$911$	−40072.0			−1.45735			−0.728675	+	0.684860i	$0.759864\pi$
$912$		0			0
$913$	−3542.85	−	6136.40i	−0.128424	−	0.222437i
$914$	−566.039	−	980.408i	−0.0204846	−	0.0354803i
$915$		0			0
$916$	−21996.5			−0.793432
$917$		0			0
$918$		0			0
$919$	10908.7	−	18894.5i	0.391562	−	0.678206i	−0.601094	−	0.799179i	$-0.705268\pi$
$919$	10908.7	−	18894.5i	0.391562	−	0.678206i	0.992656	+	0.120973i	$0.0386015\pi$
$920$	−6628.96	−	11481.7i	−0.237555	−	0.411457i
$921$		0			0
$922$	6571.18	−	11381.6i	0.234718	−	0.406544i
$923$	−23232.5			−0.828501
$924$		0			0
$925$	−55992.0			−1.99028
$926$	−7522.18	+	13028.8i	−0.266948	+	0.462368i
$927$		0			0
$928$	4855.13	+	8409.33i	0.171743	+	0.297467i
$929$	5988.52	−	10372.4i	0.211493	−	0.366317i	−0.740689	−	0.671848i	$-0.765501\pi$
$929$	5988.52	−	10372.4i	0.211493	−	0.366317i	0.952182	+	0.305532i	$0.0988341\pi$
$930$		0			0
$931$		0			0
$932$	16315.8			0.573435
$933$		0			0
$934$	−8646.69	−	14976.5i	−0.302921	−	0.524675i
$935$	45571.9	+	78932.9i	1.59397	+	2.76083i
$936$		0			0
$937$	15155.2			0.528389			0.264194	−	0.964469i	$-0.414894\pi$
$937$	15155.2			0.528389			0.264194	+	0.964469i	$0.414894\pi$
$938$		0			0
$939$		0			0
$940$	−12349.0	+	21389.2i	−0.428491	+	0.742168i
$941$	−3477.20	−	6022.69i	−0.120461	−	0.208644i	0.799489	−	0.600681i	$-0.205104\pi$
$941$	−3477.20	−	6022.69i	−0.120461	−	0.208644i	−0.919949	+	0.392037i	$0.871771\pi$
$942$		0			0
$943$	−3426.67	+	5935.16i	−0.118333	+	0.204958i
$944$	2044.39			0.0704865
$945$		0			0
$946$	2149.29			0.0738682
$947$	−4778.75	+	8277.03i	−0.163979	+	0.284020i	−0.936292	−	0.351222i	$-0.885766\pi$
$947$	−4778.75	+	8277.03i	−0.163979	+	0.284020i	0.772313	+	0.635242i	$0.219100\pi$
$948$		0			0
$949$	−6308.79	−	10927.1i	−0.215798	−	0.373772i
$950$	3501.43	−	6064.65i	0.119580	−	0.207119i
$951$		0			0
$952$		0			0
$953$	−8437.24			−0.286788			−0.143394	−	0.989666i	$-0.545802\pi$
$953$	−8437.24			−0.286788			−0.143394	+	0.989666i	$0.545802\pi$
$954$		0			0
$955$	−8021.90	−	13894.3i	−0.271814	−	0.470796i
$956$	4929.61	+	8538.33i	0.166773	+	0.288859i
$957$		0			0
$958$	−13080.9			−0.441153
$959$		0			0
$960$		0			0
$961$	−3907.84	+	6768.58i	−0.131175	+	0.227202i
$962$	6926.12	+	11996.4i	0.232128	+	0.402057i
$963$		0			0
$964$	10210.1	−	17684.4i	0.341126	−	0.590847i
$965$	26682.3			0.890087
$966$		0			0
$967$	52344.7			1.74074			0.870369	−	0.492401i	$-0.163881\pi$
$967$	52344.7			1.74074			0.870369	+	0.492401i	$0.163881\pi$
$968$	−26029.0	+	45083.6i	−0.864261	+	1.49694i
$969$		0			0
$970$	1759.62	+	3047.76i	0.0582454	+	0.100884i
$971$	18491.5	−	32028.2i	0.611143	−	1.05853i	−0.379905	−	0.925026i	$-0.624043\pi$
$971$	18491.5	−	32028.2i	0.611143	−	1.05853i	0.991048	−	0.133506i	$-0.0426234\pi$
$972$		0			0
$973$		0			0
$974$	6397.25			0.210453
$975$		0			0
$976$	3011.77	+	5216.54i	0.0987750	+	0.171083i
$977$	−8936.51	−	15478.5i	−0.292635	−	0.506859i	0.681797	−	0.731541i	$-0.261199\pi$
$977$	−8936.51	−	15478.5i	−0.292635	−	0.506859i	−0.974432	+	0.224683i	$0.927865\pi$
$978$		0			0
$979$	−57552.2			−1.87883
$980$		0			0
$981$		0			0
$982$	8933.76	−	15473.7i	0.290313	−	0.502838i
$983$	16872.0	+	29223.2i	0.547440	+	0.948195i	0.998449	+	0.0556750i	$0.0177311\pi$
$983$	16872.0	+	29223.2i	0.547440	+	0.948195i	−0.451009	+	0.892520i	$0.648936\pi$
$984$		0			0
$985$	−8709.13	+	15084.7i	−0.281722	+	0.487956i
$986$	−6761.29			−0.218381
$987$		0			0
$988$	3694.72			0.118972
$989$	−370.232	+	641.260i	−0.0119036	+	0.0206177i
$990$		0			0
$991$	7253.24	+	12563.0i	0.232499	+	0.402701i	0.958543	−	0.284948i	$-0.0919763\pi$
$991$	7253.24	+	12563.0i	0.232499	+	0.402701i	−0.726044	+	0.687649i	$0.758643\pi$
$992$	−18098.4	+	31347.4i	−0.579259	+	1.00331i
$993$		0			0
$994$		0			0
$995$	61134.7			1.94784
$996$		0			0
$997$	−21184.4	−	36692.5i	−0.672936	−	1.16556i	−0.977068	−	0.212929i	$-0.931700\pi$
$997$	−21184.4	−	36692.5i	−0.672936	−	1.16556i	0.304132	−	0.952630i	$-0.401634\pi$
$998$	−3013.20	−	5219.01i	−0.0955723	−	0.165536i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.e.x.226.3		8
3.2	odd	2	inner	441.4.e.x.226.2		8
7.2	even	3		441.4.a.v.1.2		4
7.3	odd	6		63.4.e.d.46.3	yes	8
7.4	even	3	inner	441.4.e.x.361.3		8
7.5	odd	6		441.4.a.w.1.2		4
7.6	odd	2		63.4.e.d.37.3	yes	8
21.2	odd	6		441.4.a.v.1.3		4
21.5	even	6		441.4.a.w.1.3		4
21.11	odd	6	inner	441.4.e.x.361.2		8
21.17	even	6		63.4.e.d.46.2	yes	8
21.20	even	2		63.4.e.d.37.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.e.d.37.2	✓	8	21.20	even	2
63.4.e.d.37.3	yes	8	7.6	odd	2
63.4.e.d.46.2	yes	8	21.17	even	6
63.4.e.d.46.3	yes	8	7.3	odd	6
441.4.a.v.1.2		4	7.2	even	3
441.4.a.v.1.3		4	21.2	odd	6
441.4.a.w.1.2		4	7.5	odd	6
441.4.a.w.1.3		4	21.5	even	6
441.4.e.x.226.2		8	3.2	odd	2	inner
441.4.e.x.226.3		8	1.1	even	1	trivial
441.4.e.x.361.2		8	21.11	odd	6	inner
441.4.e.x.361.3		8	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.799027 - 1.38396i) q^{2} +(2.72311 + 4.71657i) q^{4} +(9.14584 - 15.8411i) q^{5} +21.4878 q^{8} +O(q^{10})\)	\(q+(0.799027 - 1.38396i) q^{2} +(2.72311 + 4.71657i) q^{4} +(9.14584 - 15.8411i) q^{5} +21.4878 q^{8} +(-14.6156 - 25.3149i) q^{10} +(-30.6336 - 53.0590i) q^{11} -32.4462 q^{13} +(-4.61555 + 7.99438i) q^{16} +(-40.6644 - 70.4329i) q^{17} +(-10.4542 + 18.1072i) q^{19} +99.6206 q^{20} -97.9084 q^{22} +(16.8655 - 29.2119i) q^{23} +(-104.793 - 181.507i) q^{25} +(-25.9254 + 44.9041i) q^{26} +52.0227 q^{29} +(96.9622 + 167.943i) q^{31} +(93.3271 + 161.647i) q^{32} -129.968 q^{34} +(133.578 - 231.363i) q^{37} +(16.7064 + 28.9364i) q^{38} +(196.524 - 340.390i) q^{40} -203.176 q^{41} -21.9520 q^{43} +(166.838 - 288.971i) q^{44} +(-26.9520 - 46.6822i) q^{46} +(-123.961 + 214.706i) q^{47} -334.929 q^{50} +(-88.3547 - 153.035i) q^{52} +(-70.4131 - 121.959i) q^{53} -1120.68 q^{55} +(41.5676 - 71.9971i) q^{58} +(-110.734 - 191.797i) q^{59} +(326.263 - 565.104i) q^{61} +309.902 q^{62} +224.435 q^{64} +(-296.748 + 513.983i) q^{65} +(-302.239 - 523.493i) q^{67} +(221.468 - 383.593i) q^{68} +716.031 q^{71} +(194.438 + 336.777i) q^{73} +(-213.465 - 369.731i) q^{74} -113.872 q^{76} +(144.871 - 250.923i) q^{79} +(84.4263 + 146.231i) q^{80} +(-162.343 + 281.186i) q^{82} +115.652 q^{83} -1487.64 q^{85} +(-17.5403 + 30.3806i) q^{86} +(-658.249 - 1140.12i) q^{88} +(469.682 - 813.513i) q^{89} +183.707 q^{92} +(198.096 + 343.112i) q^{94} +(191.225 + 331.212i) q^{95} -120.394 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{4}+O(q^{10}) \) 8 * q - 6 * q^4	\( 8 q - 6 q^{4} + 22 q^{10} - 204 q^{13} + 102 q^{16} + 222 q^{19} - 172 q^{22} - 366 q^{25} + 220 q^{31} - 2040 q^{34} + 374 q^{37} + 822 q^{40} - 1676 q^{43} - 1716 q^{46} - 40 q^{52} - 5020 q^{55} + 1694 q^{58} + 1332 q^{61} - 1372 q^{64} - 1890 q^{67} + 1750 q^{73} - 4912 q^{76} - 8 q^{79} + 2480 q^{82} - 2232 q^{85} - 2682 q^{88} - 1416 q^{94} - 6020 q^{97}+O(q^{100}) \) 8 * q - 6 * q^4 + 22 * q^10 - 204 * q^13 + 102 * q^16 + 222 * q^19 - 172 * q^22 - 366 * q^25 + 220 * q^31 - 2040 * q^34 + 374 * q^37 + 822 * q^40 - 1676 * q^43 - 1716 * q^46 - 40 * q^52 - 5020 * q^55 + 1694 * q^58 + 1332 * q^61 - 1372 * q^64 - 1890 * q^67 + 1750 * q^73 - 4912 * q^76 - 8 * q^79 + 2480 * q^82 - 2232 * q^85 - 2682 * q^88 - 1416 * q^94 - 6020 * q^97

Introduction

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